Latest Extreme Time Machine

I would start by connecting this USB HDD to your Mac mini and use the Disk Utility to verify that it is formatted for: Mac OS Extended (Case Sensitive, Journaled)

Once verified, connect it to the 802.11ac AirPort Extreme base station's USB port. Use the AirPort Utility to share it out. Also verify that the HDD appears in the Partitions window as the correct type. I would recommend using "With a disk password" for the Secure Shared Disks setting. (see example image below)

Unfortunately, Apple's information on this question is about as clear as mud.

First, the Setup Guide does not tell you that the drive must be formatted in Mac OS Extended (Journaled) to be used with Time Machine

Second, the guide does not mention that it is often necessary to use a powered USB hub with a drive when connected to the AirPort Extreme since the USB port is borderline as far as its ability to supply sufficient power to the drive.....even if the drive has its own power supply.

But, perhaps most frustrating of all.....

The Setup Guide for the new AirPort Extreme indicates that the Extreme will support Time Machine backups to an attached USB drive......yet.....another Apple support document says that you cannot use the AirPort Extreme with an attached drive to perform Time Machine backups. Verify here:

http://support.apple.com/kb/HT2038

We have repeatedly asked Apple for clarification on this issue, but have received no response. You may have better luck if you speak with Apple directly.

When connected to the Extreme does the HDD show up properly in the AirPort Utility? Similar to the image I provided earlier?

Did you try a powered USB hub with the AirPort Extreme?

I have 3 hard drives here, and they all work fine when connected directly to a Mac....but....none of the drives will work when I connect them to the USB port on the AirPort Extreme....unless...I use a powered USB hub.

The page 13 instructions are clearly saying the opposite ofhttp://support.apple.com/kb/HT2038

That is what I already pointed out in my response above.

The Setup Guide for the new AirPort Extreme indicates that the Extreme will support Time Machine backups to an attached USB drive......yet.....another Apple support document says that you cannot use the AirPort Extreme with an attached drive to perform Time Machine backups.

So, which is correct?

When I visited two different Apple Stores and spoke to the genius types there, I received two different answers. Was finally told that I needed to call Apple Support directly.

When I contacted Apple Support by phone about 6 weeks ago with this question, I was told one thing. When I called to confirm...so that I could answer another similar question to yours.....and spoke to another support person.....I was given a different answer.

The follow up call that was promised by Apple a month ago has still not come, so we have a difficult time answering questions like yours.

Same issue but resolved. First open each airport attached, usb powered, drive/partition through finder if available. They should then appear in time machine. Best of luck. This issue has been very frustrating and finally resolved...

We did finally get clarification (sort of) from Apple on this several months ago.

As it turns out, Time Machine backups are officially supported with the new AirPort Extreme 802.11ac.

Time Machine backups are still not officially supported on earlier versions of the AirPort Extreme. That doesn't necessarily mean that they won't work, it means that you will get no help from Apple if you have a problem with this.

Some users have been able to make Time Machine backups work on the earlier versions of the AirPort Extreme with an attached USB disk, and some......like me.....were not ever able to get this working reliably.

If you have things working reliably with an earlier version of the AirPort Extreme and an attached USB disk, then you are one of the lucky ones. Congrats.